Question

1. given the equation $3x^2 - 21 = 222$, what is one exact solution? $x = \underline{\quad\quad}$

Explanation:

Step1: Isolate the \(x^2\) term

First, add 21 to both sides of the equation \(3x^2 - 21 = 222\).

$$ 3x^2 - 21 + 21 = 222 + 21 $$

Simplifying both sides, we get:

$$ 3x^2 = 243 $$

Step2: Solve for \(x^2\)

Divide both sides by 3 to solve for \(x^2\):

$$ \frac{3x^2}{3} = \frac{243}{3} $$

Simplifying, we have:

$$ x^2 = 81 $$

Step3: Solve for \(x\)

Take the square root of both sides. Remember that when we take the square root of a number, we get both a positive and a negative solution.

$$ x = \pm\sqrt{81} $$

Since \(\sqrt{81} = 9\), the solutions are \(x = 9\) or \(x = -9\). We can choose one of them, for example, \(x = 9\).

Answer:

\(9\) (or \(-9\) is also correct)